An approximate high-dimensional optimization method using hierarchical design space reduction strategy

一种基于多层设计空间缩减策略的近似高维优化方法

¹ School of Marine Science and Technology, Northwestern Polytechnical University, Xi'an 710072, China
² Key Laboratory for Unmanned Underwater Vehicle, Northwestern Polytechnical University, Xi'an 710072, China
³ Luoyang Institute of Electro-Optical Equipment, AVIC, Luoyang 471000, China

Received: 14 May 2020

Abstract

To overcome the complicated engineering model and huge computational cost, a hierarchical design space reduction strategy based approximate high-dimensional optimization(HSRAHO) method is proposed to deal with the high-dimensional expensive black-box problems. Three classical surrogate models including polynomial response surfaces, radial basis functions and Kriging are selected as the component surrogate models. The ensemble of surrogates is constructed using the optimized weight factors selection method based on the prediction sum of squares and employed to replace the real high-dimensional black-box models. The hierarchical design space reduction strategy is used to identify the design subspaces according to the known information. And, the new promising sample points are generated in the design subspaces. Thus, the prediction accuracy of ensemble of surrogates in these interesting sub-regions can be gradually improved until the optimization convergence. Testing using several benchmark optimization functions and an airfoil design optimization problem, the newly proposed approximate high-dimensional optimization method HSRAHO shows improved capability in high-dimensional optimization efficiency and identifying the global optimum.

摘要

针对高维昂贵黑箱问题(high-dimensional expensive black-box，HEB)处理过程中工程模型复杂、计算量大的难题，提出一种基于多层设计空间缩减策略的近似高维优化方法(hierarchical design space reduction strategy based approximate high-dimensional optimization method，HSRAHO)。利用3种经典代理模型：多项式响应面模型、径向基函数模型和克里金模型，使用基于预测均方根误差权重因子优化方法计算获得各代理模型权系数，通过加权叠加构建组合代理模型，替代实际高维黑箱模型。使用多层设计空间缩减策略根据已知信息确定设计子空间，并在其内部确定有效样本点，逐步提高组合代理模型在感兴趣区域的预测精度，直至优化收敛。将提出的近似高维优化方法HSRAHO应用于标准优化函数和翼型设计优化问题，测试结果验证了该方法在高维优化效率和全局收敛性方面的优势。